Phase transition for the frog model

We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1-p. When an active particle hits a sleeping particle, the latter becomes active. Phase transition results and asymptotic values for critical parameters are presented for Z^d and regular trees

Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons

We consider a complex vector bundle E endowed with a connection A over the eight-dimensional manifold R^2 x G/H, where G/H = SU(3)/U(1)xU(1) is a homogeneous space provided with a never integrable almost complex structure and a family of SU(3)-structures. We establish an equivalence between G-invariant solutions A of the Spin(7)-instanton equations on R^2 x G/H and general solutions of non-Abelian coupled vortex equations on R^2. These vortices are BPS solitons in a d=4 gauge theory obtained from N=1 supersymmetric Yang-Mills theory in ten dimensions compactified on the coset space G/H with an SU(3)-structure. The novelty of the obtained vortex equations lies in the fact that Higgs fields, defining morphisms of vector bundles over R^2, are not holomorphic in the generic case. Finally, we introduce BPS vortex equations in N=4 super Yang-Mills theory and show that they have the same feature.Comment: 14 pages; v2: typos fixed, published versio

Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory

It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R^{3,1}. We show that such solutions exist in SU(N) gauge theory on the spaces R^2\times S^2 and R^1\times S^1\times S^2 with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on T^1\times S^2, where T^1 is R^1 or S^1. Namely, imposing SO(3)-invariance and some reality conditions, we consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the \phi^4 kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R^{1,1}\times S^2 via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on R^1\times S^1 admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S^1 with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space R^1\times S^1\times S^2 which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). We also describe similar solutions in Euclidean SU(N) gauge theory on S^1\times S^3 interpreted as chains of n instanton-antiinstanton pairs.Comment: 16 pages; v2: subsection on topological charges added, title expanded, some coefficients corrected, version to appear in PR

Effects of Sequence Disorder on DNA Looping and Cyclization

Effects of sequence disorder on looping and cyclization of the double-stranded DNA are studied theoretically. Both random intrinsic curvature and inhomogeneous bending rigidity are found to result in a remarkably wide distribution of cyclization probabilities. For short DNA segments, the range of the distribution reaches several orders of magnitude for even completely random sequences. The ensemble averaged values of the cyclization probability are also calculated, and the connection to the recent experiments is discussed.Comment: 8 pages, 4 figures, LaTeX; accepted to Physical Review E; v2: a substantially revised version; v3: references added, conclusions expanded, minor editorial corrections to the text; v4: a substantially revised and expanded version (total number of pages doubled); v5: new Figure 4, captions expanded, minor editorial improvements to the tex

Effects of Kinks on DNA Elasticity

We study the elastic response of a worm-like polymer chain with reversible kink-like structural defects. This is a generic model for (a) the double-stranded DNA with sharp bends induced by binding of certain proteins, and (b) effects of trans-gauche rotations in the backbone of the single-stranded DNA. The problem is solved both analytically and numerically by generalizing the well-known analogy to the Quantum Rotator. In the small stretching force regime, we find that the persistence length is renormalized due to the presence of the kinks. In the opposite regime, the response to the strong stretching is determined solely by the bare persistence length with exponential corrections due to the ``ideal gas of kinks''. This high-force behavior changes significantly in the limit of high bending rigidity of the chain. In that case, the leading corrections to the mechanical response are likely to be due to the formation of multi-kink structures, such as kink pairs.Comment: v1: 16 pages, 7 figures, LaTeX; submitted to Physical Review E; v2: a new subsection on soft kinks added to section Theory, sections Introduction and Conclusions expanded, references added, other minor changes; v3: a reference adde

Symmetric Rotating Wave Approximation for the Generalized Single-Mode Spin-Boson System

The single-mode spin-boson model exhibits behavior not included in the rotating wave approximation (RWA) in the ultra and deep-strong coupling regimes, where counter-rotating contributions become important. We introduce a symmetric rotating wave approximation that treats rotating and counter-rotating terms equally, preserves the invariances of the Hamiltonian with respect to its parameters, and reproduces several qualitative features of the spin-boson spectrum not present in the original rotating wave approximation both off-resonance and at deep strong coupling. The symmetric rotating wave approximation allows for the treatment of certain ultra and deep-strong coupling regimes with similar accuracy and mathematical simplicity as does the RWA in the weak coupling regime. Additionally, we symmetrize the generalized form of the rotating wave approximation to obtain the same qualitative correspondence with the addition of improved quantitative agreement with the exact numerical results. The method is readily extended to higher accuracy if needed. Finally, we introduce the two-photon parity operator for the two-photon Rabi Hamiltonian and obtain its generalized symmetric rotating wave approximation. The existence of this operator reveals a parity symmetry similar to that in the Rabi Hamiltonian as well as another symmetry that is unique to the two-photon case, providing insight into the mathematical structure of the two-photon spectrum, significantly simplifying the numerics, and revealing some interesting dynamical properties.Comment: 11 pages, 5 figure

On Explicit Point Multi-Monopoles in SU(2) Gauge Theory

It is well known that the Dirac monopole solution with the U(1) gauge group embedded into the group SU(2) is equivalent to the SU(2) Wu-Yang point monopole solution having no Dirac string singularity. We consider a multi-center configuration of m Dirac monopoles and n anti-monopoles and its embedding into SU(2) gauge theory. Using geometric methods, we construct an explicit solution of the SU(2) Yang-Mills equations which generalizes the Wu-Yang solution to the case of m monopoles and n anti-monopoles located at arbitrary points in R^3.Comment: 1+7 pages, LaTe

Giant Pulses with Nanosecond Time Resolution detected from the Crab Pulsar at 8.5 and 15.1 GHz

We present a study of shape, spectra and polarization properties of giant pulses (GPs) from the Crab pulsar at the very high frequencies of 8.5 and 15.1 GHz. Studies at 15.1 GHz were performed for the first time. Observations were conducted with the 100-m radio telescope in Effelsberg in Oct-Nov 2007 at the frequencies of 8.5 and 15.1 GHz as part of an extensive campaign of multi-station multi-frequency observations of the Crab pulsar. A selection of the strongest pulses was recorded with a new data acquisition system, based on a fast digital oscilloscope, providing nanosecond time resolution in two polarizations in a bandwidth of about 500 MHz. We analyzed the pulse shapes, polarisation and dynamic spectra of GPs as well as the cross-correlations between their LHC and RHC signals. No events were detected outside main pulse and interpulse windows. GP properties were found to be very different for GPs emitted at longitudes of the main pulse and the interpulse. Cross-correlations of the LHC and RHC signals show regular patterns in the frequency domain for the main pulse, but these are missing for the interpulse GPs. We consider consequences of application of the rotating vector model to explain the apparent smooth variation in the position angle of linear polarization for main pulse GPs. We also introduce a new scenario of GP generation as a direct consequence of the polar cap discharge. We find further evidence for strong nano-shot discharges in the magnetosphere of the Crab pulsar. The repetitive frequency spectrum seen in GPs at the main pulse phase is interpreted as a diffraction pattern of regular structures in the emission region. The interpulse GPs however have a spectrum that resembles that of amplitude modulated noise. Propagation effects may be the cause of the differences.Comment: Astronomy & Astrophysics (accepted